In the astrophysical high-temperature environment the excited states of nuclei involved are thermally populated, which can also contribute to the total reaction
rate [1]}, [2]}. The first excited state in \(^7\) Be is located at 429 keV, which is too high to make appreciable contribution in the total rate
comparing to the ground state at BBN temperature region. Thus, it is appropriate to calculate the thermonuclear rate of \(^7\) Be(n,\(\alpha \) )\(^4\) He by taking only
the ground state of \(^7\) Be nucleus into account. Relying on the first term of Eq. (REF ), we have directly derived the cross section of
\(^4\) He(\(\alpha \) ,\(n\) )\(^7\) Be (g.s.) by utilizing those data of \(^4\) He(\(\alpha \) ,\(p\) )\(^7\) Li (g.s.) listed in Table REF .
It is worthy of noting that the ground-state contribution required is difficult to be extracted from the total cross section measured [3]} for
\(^4\) He(\(\alpha \) ,\(n\) )\(^7\) Be, and also these data were only measured down to \(E_\alpha \) =39.43 MeV which is much higher than those measured for
\(^4\) He(\(\alpha \) ,\(p\) )\(^7\) Li.
